منابع مشابه
Extremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric
A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...
متن کاملSolving Geometric Optimization Problems
We show how to use graphics hardware for tackling optimization problems arising in the field of computational geometry. We exemplarily discuss three problems, where combinatorial algorithms are inefficient or hard to implement. Given a set S of n point in the plane, the first two problems are to determine the smallest homothetic scaling of a star shaped polygon P enclosing S and to find the lar...
متن کاملTwo Geometric Optimization Problems
We consider two optimization problems with geometric structures The rst one con cerns the following minimization problem termed as the rectilinear polygon cover problem Cover certain features of a given rectilinear polygon possibly with rectilinear holes with the minimum number of rectangles included in the polygon Depending upon whether one wants to cover the interior boundary or corners of th...
متن کاملT Geometric Intersection Problems
We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine i to detect whether two simple plane polygons intersect. We employ...
متن کاملSome Geometric Clustering Problems
This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP-hard. On the other hand, we identify several special cases that are solvable in polynomial time due to t...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1984
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(84)80040-6